Discussion area to prepare for Exam 2
To find the radius of convergence of $ \sum_{n=0}^\infty (n!)z^{n!} $, you'll need to use the Ratio Test.
$ \frac{u_{n+1}}{u_n}=\frac{(n+1)!z^{(n+1)!}}{n!z^{n!}}=(n+1)z^{n\cdot n!} $.
Ask yourself what that does as n goes to infinity in case |z|<1, =1, >1. You might recall that $ nr^n\to 0 $ as $ n\to\infty $ if $ |r|<1 $. --Steve Bell
